Emergence of Antiferromagnetic Correlation in LiTiVO via Li NMR\abst
We report Li NMR studies of V-substitution effects on spinel oxide superconductor LiTiO ( = 13.4 K). In LiTiVO ( = 0 0.4), the V substitution for the Ti site suppressed the relative volume fraction of superconductivity faster than . From the observation of fairly homogeneous enhancement in a Li nuclear spin-lattice relaxation rate, we conclude that the V substitution changes electron correlation effects through electron carrier doping from quarter electron filling 3 to 3 and then the antiferromagnetic correlation emerges. \kwordLiTiO, NMR, vanadium substitution, antiferromagnetic spin fluctuation
Transition-metal spinels have attracted great interests, because intriguing electronic phases and their competition are associated with frustration effects on spin, charge, orbital networks and the coupling with crystal lattice . A normal spinel LiTO is a type-II oxide superconductor with a high 13 K [2, 3]. The crystal structure is stable at low temperatures. LiTiO is an -wave superconductor, because of a Hebel-Slichter peak in Li nuclear spin-lattice relaxation rate  and activation-type specific heat . The mystery is the unconventional break down of the superconductivity. Although the coherence length is long enough , the superconductivity is suppressed as the decrease in the superconducting volume fraction for Li-deficient LiTiO  and Li-rich LiTiO [2, 7]. The Li deficiency and Li substitution for Ti site make the conduction band from the quarter filling to the band insulating states.
The full solid solution of LiTiVO (0 2) is known . An itinerant-electron spinel LiVO shows a heavy electronic specific heat and a Curie-Weiss spin susceptibility . Although the ferromagnetic spin fluctuations were estimated from NMR data , the antiferromagnetic fluctuations were observed at low temperatures by neutron scattering experiments [11, 12]. The spin fluctuation spectrum may not be simple [12, 13]. Ti substitution for LiVO induces spin-glass-like behaviors and the microscopic effects were studied . The microscopic effects of V substitution for LiTiO, however, have been poorly understood.
One may expect two electronic effects of V substitution for Ti sites in LiTiO. One is a simple pair-breaking effect of additional impurity electron spin = 1 on the superconductivity. The V electrons are assumed to have localized moments. The randomly distributed local moments can induce non-exponential NMR relaxation [15, 16, 17, 18]. The other is the carrier doping effect on electron correlation through band filling from quarter electron filling 3 to 3. The V electrons are assumed to hybridize the Ti conduction electrons and then to be itinerant. Even for the random crystalline potentials introduced through the substitution, NMR linewidths may be broader but the NMR relaxation can have a single spin-lattice relaxation time .
In this Letter, we report the Li NMR studies of LiTiVO ( = 0 0.4). The V substitution was found to suppress the relative volume fraction of superconductivity faster than and to enhance fairly homogeneously and largely the Li nuclear spin-lattice relaxation but not so much the Knight shift. The antiferromagnetic correlation was concluded to emerge in the V substituted samples.
Powder samples of LiTiVO were synthesized by a solid state reaction method with a precursor of LiTiO, because Ti is easily oxidized to be Ti . First, LiTiO was synthesized from the mixture of preheated dry LiCO (99.9 ) and TiO (99.99 ) after ref. 7. Next, the mixtures of LiTiO, TiO, Ti and VO were sealed in evacuated quartz tubes and then fired at 760 C for 00.04, at 800 C for 0.080.16, and at 850 C for 0.20.4 in a week. The powder X-ray diffraction patterns indicated all the samples of 0.04 in a single phase with spinel structure and the samples of 0.08 with a small amount of unreacted VO. The cryopreservation method at 77 K in liquid nitrogen was employed to keep the samples fresh.
We performed high resolution Fourier-transformed Li (nuclear spin = 3/2 and nuclear gyromagnetic ratio /2 = 16.546 MHz/T) NMR measurements of free induction decay signals or the nuclear spin-echoes at = 7.48414 T. The applied magnetic field was estimated from the reference material LiCl. Nuclear spin-lattice relaxation times were measured by an inversion recovery technique.
Magnetization was measured by a SQUID magnetometer (Quantum Design MPMS) for = 0, 0.01, 0.02, 0.04, 0.08, 0.16, 0.2 and 0.4. Figure 1 (a) shows uniform magnetic susceptibility at 100 G after cooling in a zero field (ZFC) and in a field of 100 G (FC) for LiTiVO with = 0, 0.08, 0.12, 0.16, 0.2. The temperature hysteresis and the onset of diamagnetic response in diminished for 0.12. Figure 1 (b) shows V concentration dependence of and the relative volume fraction of superconductivity to = 0 at 5 K. The V impurities suppress the relative volume fraction faster than .
Low field magnetization curves were non-linear even at 300 K, but high field ones ( 0.5 T) were linear. Thus, we defined the intrinsic magnetic susceptibility of LiTiVO in the normal states by the difference in magnetization at = 4 and 5 T, . The non-linear magnetization at lower fields than 0.4 T might be due to unintentional magnetic impurities (minute impurity phase). Figure 2 shows paramagnetic susceptibility for = 0, 0.04 and 0.16. The V impurities induce Curie-Weiss like behaviors .
Figure 3 shows Li NMR frequency spectra as a function of temperature for = 0 (a) and = 0.08 (b). All the Li NMR spectra except = 0 below are symmetric. No quadrupole splits are observed. The peak frequencies show negative shifts and decrease as temperature is decreased. The linewidths are broadened by the V substitution. This evidences the actual substitution of the V ions for the Ti ions.
Figure 3(c) shows the temperature dependences of Li Knight shifts in LiTiVO ( 0.16). The negative shifts show Curies-Weiss behaviors. The Li Knight shift of Curies-Weiss sort in LiVO was positive .
In Fig. 4, Li Knight shifts are plotted against magnetic susceptibility defined by / at = 4 and 5 T, where temperature is an implicit parameter, for LiTiVO with = 0, 0.04 and 0.16. The inset shows on an expanded scale the plot of pure LiTiO.
The Li Knight shift consists of a spin shift and a chemical shift ,
The spin shift is expressed by a product of a hyperfine coupling constant and a temperature dependent spin susceptibility
where is the Avogadro number and is the Bohr magneton.
The bulk magnetic susceptibility is given by
where is the Van Vleck orbital susceptibility and is the diamagnetic susceptibility of inner core electrons.
In Fig. 4, the solid lines are the least-squares fitting results by = + ( and are the fit parameters). The linear relation between and breaks down at lower temperatures for = 0.04 and 0.16. The bulk magnetic susceptibility must include Curie components being different from the peak Knight shifts of the broadened Li NMR spectra.
From the fitting results, the hyperfine coupling constant was estimated to be 3.12, 1.05 and 0.74 kOe/Ti for = 0, 0.04 ( 100 K) and 0.16 ( 200 K), respectively. In passing, the of LiVO is positive . From = 6.2810 emu/f.u.mole and tentative = 3.3310 emu/f.u.mole , the chemical shift was estimated to be positive 0.002 0.005 . Although the magnitude of depends on the choice of , the positive chemical shift is unconventional.
Figure 5 shows the Li nuclear spin-lattice relaxation curves (recovery curves) ( is the time after an inversion pulse to the observation pulse and is the nuclear magnetization) for LiTiVO ( = 0 0.4). The solid curves are the results of the least-squares fitting using a stretched exponential function
where , and are the fit parameters. As seen in Fig. 5, the recovery curves for the V substitution are nearly single exponential functions except the low temperature for = 0.2. The V substitution enhances 1/ while keeping nearly the homogeneous spin-lattice relaxation.
Figure 6(a) shows the temperature dependence of for = 0 0.4. For 0.2, the exponent 0.8 is nearly independent of temperature, while for = 0.2 and 0.4, the cooling down below 50 K leads to 0.5. For the Li poor and rich samples, we observed 0.5 immediately when the Li deficiency and the Li substitution for Ti site  are introduced into LiTiO. Thus, nearly the single exponential functions exclude the deviation of Li composition. The observed V impurity effect at the high magnetic field 7.5 T for 0.2 is in contrast to the conventional magnetic impurity effect on the NMR relaxation, where the non-exponential recovery curves are induced only at low fields and low temperatures ( =1 at 300 K is reduced to 0.5 at low temperatures) and easily suppressed by the high magnetic field of 7.5 T [15, 16].
Figure 6(b) shows the temperature dependence of 1/ for = 0 0.4. For pure LiTiO, 1/ shows dependence. With the V substitution, 1/ is highly enhanced and the temperature dependence below 100 K is changed into with 0.7. Evidently, the enhancement of 1/ due to the V substitution is larger than that of the magnitude of the Knight shift . That is the emergence of the antiferromagnetic correlation.
Electron correlation changes the Korringa ratio . The modified Korringa relation is characterized by
where is the electron gyromagnetic ratio and is the exchange enhancement factor . The value of is associated with the wave vector () dependence of a generalized spin susceptibility (, ), that is the ratio of the -averaged () to the uniform ( = 0). The ferromagnetic and antiferromagnetic () lead to 1 and 1, respectively. Incommensurately enhanced () also leads to 1.
One should note that the dependence of the hyperfine coupling constant also plays a significant role. A Li site (8a) has 12 nearest neighbor Ti sites (16d). The 12 Ti ions located at the corners of a truncated tetrahedron surround the Li ion at the center of the tetrahedron in a cubic spinel. Thus, the staggered magnetic fields from the Ti electrons on four sublattices may be cancelled out and masked at the Li site. The dependent can work as a filter to the staggered mode.
Figure 7 shows the V substitution effect on the modified Korriga ratio defined by eq.( 5). The V substitution changes 1 for pure LiTiO into 1. The emergence of the antiferromagnetic correlation due to the V substitution, not a conventional quantum phase transition, was seen through the Li NMR. One should note that the enhanced 1/ may be due to incommensurate magnetic correlation, which is not filtered by .
The V substitution effect is not a simple pair-breaking effect on the superconductivity but also the change of the electron correlation effect of the 3 band from 3 filling to 3. The electron carrier doping via V substitution is consistent with the sign of Seebeck coefficient .
In conclusion, we observed V-induced enhancement in Li nuclear spin-lattice relaxation rates in LiTiVO ( = 0 0.4), which indicates the emergence of the antiferromagnetic correlation. The V substitution for Ti ions changes the electron correlation effects by controlling the band filling from quarter electron filling 3 to 3.
We thank T. Waki, H. Chudo, H. Ohta, A. Tanizawa, C. Michioka for their experimental assistance and helpful discussions. This work was supported in part by a Grant-in-Aid for Science Research on Priority Area, “Invention of Anomalous Quantum Materials,” from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Grant No. 16076210) and in part by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (Grant No. 19350030).
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